How to export to FBX without baking animations?
Unfortunately, no; as far as I know, you can't export unbaked raw animation using the FBX exporter.

According to this post, unchecking Baked Animation disables all animation export, meaning the FBX is created without any animation information at all.  I realize it's tantalizing that perhaps disabling baked animation would have somehow exported keyframed "unbaked" animation, but that's unfortunately not the case with this particular exporter.  Unchecking this option works like an off switch with respect to animation.  Check it and you get baked animation, uncheck it and you get no animation.  :(